Remo Freuler's brilliant goal early in the second half sent the Swiss through to the knockout rounds for the fourth time in five World Cups.
Premier League: Liverpool took to social media to thank Xherdan Shaqiri for his time at the Merseyside club. The Swiss player has completed a move to Lyon.
Jose Mourinho said he accepted responsibility for a 5th defeat of the season that leaves Manchester United 11 points adrift of even a top-four finish.
Daniel Sturridge stunned Chelsea with a late goal to rescue a point for Liverpool.
Mohamed Salah got Liverpool up and running as they comfortably dispatched West Ham in their first Premier League fixture of the season.
Shaqiri was one of five recent high profile signings which saw Liverpool shell out more than 200 million pounds in an attempt to close the gap on Premier League champions Manchester City.
The club have spent 174 million pounds ($229 million) on midfielders Naby Keita and Fabinho, winger Xherdan Shaqiri and, perhaps most crucially, Brazil goalkeeper Alisson.
Xhaka and Shaqiri celebrated their goals by making a "double eagle" gesture with their hands to represent the Albanian flag.
The win puts Switzerland in pole position to make it out of a tough Group E.
World Cup 2018, Brazil vs Switzerland Highlights: Brazil were held to a 1-1 draw against Switzerland at the Rostov Arena